Log into your account at github (if you don't have one, create one), and click on "Create a new repo". There you should enter a good name for your repository (I suggest "dotfiles" or similar) and - if you want - a description. Then click on "create repository". Done ;)

In case you haven't done so already, you should add the public SSH keys of your machines to the list of authorized keys, otherwise you won't be able to commit to your git repositories using SSH.
(In short, you have to copy the contents of ~/.ssh/id_dsa.pub into the box at the github site. If you have no idea what I'm talking about, better read up on SSH public key authentication.)

Step 2: Initialize the dotfiles directory and repository

At first, you need to create the .dotfiles directory and move the dotfiles that you want to put under revision control there.

where "YOUR NAME" and yourmail@something.com are the name and mail address with which your commits will be signed. You don't have to do this and you don't have to provide your real name or address there. Decide for yourself.
But GITUB_USERNAME has to be your github username (who would have guessed ...).

Step 3: Track changes with git

Now and whenever you have changed something in your .dotfiles folder, add those changes or files to the repository and push it to github.

I haven't thought about whether I want to automate this step and how. For the moment, manually pulling changes from github seems the best solution to me, since I'm not changing my dotfiles on a daily basis.

git pull origin master

and sometimes

~/dotfiles/symlinks.sh

if you just added the machine to the management system or if new dotfiles have been put under revision control.

Addtional remarks

I've found it to be more comfortable to github as upstream repository with

git push -u origin master

because after that I only have to use

git push

and

git pull

Also, I wrote this article bases on the bash histories of my machines, so in case you encounter an error, please tell me so in the comments so that I can correct this article. Thanks ;)